The units of energy and the conversions that matter

Framing

Open an oil major's annual report and production is in millions of barrels a day, reserves in billions of barrels, the carbon footprint in millions of tonnes of CO₂. Open a power utility's report and the same company's cousin measures generation in terawatt-hours, capacity in gigawatts and your bill in kilowatt-hours. Open a long-term gas contract and the price is in dollars per million British thermal units. Open the International Energy Agency's flagship outlook and the whole world's energy runs in exajoules. Four documents, four vocabularies, one physical quantity.

Lesson 1.1 established that energy is a single scalar quantity: additive across forms, governed by two laws, the same whether it sits in a barrel of oil or a battery. The awkward practical fact is that this one quantity is sold, taxed, traded and tabulated in at least a dozen different units, and most of them were invented before the metric system, by people who have never once agreed to stop using them. Translating between them on sight is the difference between a professional and an informed bystander.

The fluency is not academic. A trader who reads gas in dollars per MMBtu and power in euros per megawatt-hour cannot tell whether the spark spread is open without converting one into the other. An analyst who sees a liquefaction plant rated at 8 million tonnes a year and a terminal rated at 12 billion cubic metres a year cannot tell whether the deal balances until both sit in the same unit. By the end of this lesson you will be able to take any of those figures and land it, correctly, in any of the others.

Key terms

The terms appear in the order the lesson uses them. Each is the SI definition or the industry convention, with the exact factor where one exists.

1. Joule (J). The SI unit of energy. One joule is the work done when a force of one newton acts through one metre. It is the only unit here defined by physics; every other unit in this lesson is a convention bolted onto it.
2. Watt (W). The SI unit of power: one joule per second. Power is the rate at which energy flows; energy is the amount that has flowed. A 1 GW power station can deliver one gigawatt; it produces energy only while it is actually running. Watt and watt-hour are not interchangeable, and confusing them is the single most common mistake in public energy talk.
3. Watt-hour family (Wh, kWh, MWh, GWh, TWh). The energy delivered when one watt flows for one hour, so one watt-hour is 3,600 joules. One kilowatt-hour is 3.6 megajoules — the energy a 1 kW heater puts out in an hour, which is why it ended up on your electricity bill. The terawatt-hour is the unit of national power statistics.
4. SI prefixes (kilo to exa). The decimal multipliers: kilo (10³), mega (10⁶), giga (10⁹), tera (10¹²), peta (10¹⁵), exa (10¹⁸). The industry uses every rung. A water heater is tens of kilowatt-hours; a gas platform's daily output is tens of terajoules; world demand is hundreds of exajoules.
5. British thermal unit (BTU) and MMBtu. The BTU is the imperial heat unit: the energy to raise one pound of water by one degree Fahrenheit, fixed at 1,055.06 joules. The MMBtu is one million of them, equal to 1.055 gigajoules. The "MM" is a doubled Roman numeral M (a thousand), so MM means a thousand thousand — one set of confusing notation apparently not being enough. The MMBtu prices North American gas and the global LNG trade.
6. Calorie (cal) and kilocalorie (kcal). The energy to raise one gram of water by one degree Celsius, equal to 4.186 joules. The kilocalorie is 4,186 joules — and is also, confusingly, the "calorie" printed on food packets.
7. Tonne of oil equivalent (toe) and Mtoe. The energy released by burning one tonne of reference crude, fixed by the IEA at 41.868 gigajoules on a net heating-value basis. One toe is therefore 11.63 megawatt-hours. The Mtoe is the IEA's and the OECD's working unit.
8. Barrel of oil equivalent (boe) and Mboe. The unit producers use to add up oil and gas as one number, conventionally 5.8 million BTU, or about 6.12 gigajoules, per barrel. Having invented a perfectly good reference unit in the toe, the industry promptly invented a second for the same job: 1 toe equals about 7.33 boe. The boe rules oil-major reserve disclosures.
9. Energy density. The energy released per unit of mass or of volume when a fuel burns. It is the bridge between physical units (litre, tonne, barrel) and energy units. A barrel is only a unit of volume until you name the crude; then it becomes a unit of energy.
10. Lower and higher heating value (LHV, HHV). The two ways of counting a fuel's combustion energy. The lower value counts the heat released with the exhaust water leaving as vapour; the higher value counts the extra heat you would get by condensing that water back to liquid. The gap is about 10 per cent for natural gas and 5 to 6 per cent for oil. The IEA reports on the lower basis, the US Energy Information Administration on the higher, and the choice is one of the most consequential silent assumptions in the business.

The joule, and why almost nobody uses it

Lesson 1.1 introduced the joule as the SI unit of energy. It is rigorous, additive and the reason a global energy balance is possible at all. It is also, at industrial scale, almost unusable — a beautiful unit that the working industry treats rather like Latin: foundational, universally respected, spoken by no one.

The problem is the span. A litre of petrol holds about 32 megajoules. A barrel of crude, 159 litres, holds roughly 6 gigajoules. A single cargo of liquefied natural gas holds 3.8 petajoules. World primary energy demand in 2024 was 592 exajoules, or 5.92 × 10²⁰ joules (Energy Institute 2025). That is twenty-one orders of magnitude between the petrol pump and the planet, and no one carries that range in their head in joules.

So each corner of the industry adopted a unit sized to its own daily business. The household bills in kilowatt-hours. North American gas trades in million BTU. Crude trades in barrels. The oil major reports in millions of barrels of oil equivalent. The IEA tabulates in millions of tonnes of oil equivalent. The global balance is struck in exajoules. Some of these units are pre-metric survivals, some are scaled to a household, some are pegged to a reference fuel, but all of them are the same scalar quantity in different clothes. The rest of this lesson treats the conversion factors as a single Rosetta stone — type a figure in once, read it everywhere.

Power is not energy

Before the unit families, one error has to be cleared off the table, because it underlies most bad energy journalism. Power is the rate at which energy flows. Energy is the amount that has flowed. A gigawatt is a speed; a gigawatt-hour is a distance. Confusing the two is the energy equivalent of confusing your salary with your bank balance.

A 1 GW gas plant can deliver one gigawatt at any instant it runs. Run it flat out for a year and it produces 1 GW × 8,760 hours = 8,760 GWh. Real plants never run flat out all year. A baseload nuclear unit manages a capacity factor near 90 per cent; a modern combined-cycle gas turbine 50 to 60 per cent; an onshore wind farm 30 to 40 per cent; offshore wind 45 to 55 per cent; solar around 20 per cent. Annual energy is capacity multiplied by the hours in the year multiplied by that fraction, and nothing else.

This is the arithmetic missing from every headline that announces "100 GW of new solar" as though gigawatts were a quantity of electricity rather than a rate of producing it. Internalise the watt and the watt-hour as separate things and you never make the slip again.

A working professional in power carries one more conversion as a reflex: one terawatt-hour is 3.6 petajoules. That single factor is the bridge between the electricity world and the SI world, and the IEA reports in both so that the rest of us can cross it.

The old units: BTU, calorie, toe and boe

Outside the power sector, the industry's units are older than the SI itself, and they survived for the dullest possible reason: the contracts written in them survived, and contracts are not torn up for the sake of tidy arithmetic. The British thermal unit was defined in imperial Britain, the calorie in continental Europe, and both outlived their empires because the paperwork did.

The BTU is tiny — 1,055 joules, about the energy in one wooden match. At industrial scale it becomes the MMBtu, the doubled-M million from the key terms, equal to 1.055 gigajoules. The Henry Hub contract that prices most North American gas is quoted in dollars per MMBtu, and so is the global LNG trade (S&P Global 2024). Whole continents of gas change hands in a unit named after a match.

The petroleum units are stranger still, because they start life as volume or mass and only become energy once a heating value is attached. A barrel is 159 litres of liquid; it is a quantity of energy only once you know the grade. To add up a portfolio of different crudes and gases as one figure, the industry fixed the barrel of oil equivalent at 5.8 million BTU, or 6.12 gigajoules — roughly a medium-light crude. It is not exact for any single grade, but it is close enough to aggregate a global production book. The same instinct produced the tonne of oil equivalent at the mass scale, fixed by the IEA at 41.868 gigajoules (IEA 2024a). These two reference units carry the international statistics: the IEA counts world supply in millions of tonnes of oil equivalent, the supermajors count reserves in millions of barrels of oil equivalent, and the two are locked together by definition at 1 toe = 7.33 boe. Commit four numbers to memory — 41.868 for toe, 6.12 for boe, 1.055 for MMBtu, 3.6 for the kilowatt-hour — and the rest of the unit landscape falls out in a single multiplication.

Energy density: how a litre becomes a megajoule

The barrel and the cubic metre measure volume. The tonne and the kilogram measure mass. They turn into energy only when a heating value is named, because the energy belongs to the substance, not to the container.

Measured by mass, the common fuels span a wide range. Liquefied natural gas has the highest specific energy of any large-scale carrier, around 50 MJ/kg. Diesel and jet fuel sit near 43; crude oil between 42 and 46, depending on grade; good thermal coal around 24, falling to 8 or 12 for lignite; dry wood around 16. The lithium-ion battery, the best electrochemical store in mass production, manages about 0.9 MJ/kg at the cell — which is why an electric car hauls half a tonne of battery to do the work a gym bag of diesel would do (Smil 2017, 51–59).

Measured by volume, the same fuels re-rank, and the engineering of the whole transport chain follows the volume figure. Petrol holds 32 MJ per litre, diesel 36. Liquefied natural gas, chilled to minus 162 degrees, holds 22 MJ per litre — but natural gas at room pressure holds only 38 MJ per cubic metre, six hundred times less than in its liquid form. That six-hundred-fold shrinkage is the entire reason ships can carry gas across oceans: a single 174,000 m³ carrier holds the energy of more than 100 million m³ of gas at atmospheric pressure, which would otherwise need a vessel the size of a small country. A high-pressure pipeline splits the difference, carrying about 7.6 GJ per cubic metre at 200 bar, which is why pipelines win under roughly 4,000 kilometres and liquefaction wins beyond it. The whole pipe-versus-ship question is a unit conversion wearing a hard hat.

The 10 per cent that ruins everything

Every conversion factor above rests on a silent assumption: that the heating value is the lower one. When that assumption is left unstated in a contract or a table, it quietly introduces an error of about 10 per cent for natural gas and 5 to 6 per cent for oil. People have lost real money to a footnote.

The chemistry is simple. Burn a hydrocarbon and you get carbon dioxide and water, and the water leaves up the chimney as vapour. To get back the energy locked in that vapour, you would have to cool the exhaust below its dew point and condense the water — which most plants refuse to do, because cool exhaust does less work and the condensate is acidic and eats the equipment. So the energy you actually get is the lower heating value: the gross combustion energy minus the heat carried off in the vapour.

The higher heating value counts that recovered heat in, as if the water always condensed. It is the thermodynamic ceiling. Hydrogen-rich fuels make the most combustion water, so they have the widest gap: natural gas runs about 38 MJ per cubic metre lower against 42 higher, roughly 10 per cent, while pure hydrogen runs 120 MJ/kg against 142, a full 18 per cent. Coal, with little hydrogen, has the narrowest gap, about 3 per cent.

This matters because the institutions disagree on which value they print. The IEA reports on the lower basis throughout, the US Energy Information Administration on the higher (Energy Institute 2025). Cross-reference an IEA figure against an EIA figure without converting and your numbers will refuse to balance, for a reason hidden in a methodology note nobody reads. In LNG the gap is at least written down: a sale-and-purchase agreement names the heating value, the measurement standard and the pricing basis explicitly, because on a single 76,500-tonne cargo at $12 per MMBtu, the 10 per cent gap is worth about $4 million. That is a sum worth reading the footnote for.

Worked example: one LNG cargo, in every unit

To make the Rosetta stone concrete, take one physical thing — the cargo of a standard modern LNG carrier — and write it out in every unit the industry uses for it. This is the arithmetic a professional runs, half-consciously, while reading a contract, a press release and a statistical bulletin that all describe the same ship.

The vessel is a 174,000 m³ membrane carrier, the workhorse of the modern fleet of 742 active ships (IGU 2025). It loads at Ras Laffan in Qatar for Rotterdam. Qatari LNG is lean — almost pure methane — with a specific energy of about 49.6 GJ per tonne and a liquid density near 440 kg/m³.

Step 1 — Volume to mass

174,000 m³ × 0.440 t/m³ = 76,560 tonnes, which the shipping papers round to 76,500. In the market this is "a 76,500-tonne cargo".

Step 2 — Mass to energy

76,500 t × 49.6 GJ/t = 3,794,400 GJ, or about 3.8 PJ, on a lower heating-value basis.

Step 3 — Energy in MMBtu, the contract unit

3.8 × 10¹⁵ J ÷ 1.055 × 10⁹ J/MMBtu = 3,598,000 MMBtu, about 3.6 TBtu — the figure on the invoice. At a Japan-Korea Marker of $12 per MMBtu the cargo is worth about $43.2 million; at a Title Transfer Facility price of €40 per MWh, about €42 million. The two need not agree, and the gap between them is the day job of an LNG trading desk.

Step 4 — Energy as regasified gas

3.8 × 10¹⁵ J ÷ 38 × 10⁶ J/m³ = 100 million m³ of natural gas at atmospheric pressure — the number the Dutch terminal reports to the grid operator.

Step 5 — Energy in toe, the IEA unit

3.8 × 10⁶ GJ ÷ 41.868 GJ/toe = 90,600 toe, or 0.091 Mtoe. A whole cargo registers on the IEA's annual balance as a rounding error. A year of deliveries from one Qatari contract, eight to ten cargoes, shows up as about 0.8 Mtoe.

Step 6 — Energy in boe, the oil-major unit

3,598,000 MMBtu ÷ 5.8 MMBtu/boe = 620,300 boe. At the parent company's reporting level the same cargo is 0.62 Mboe of gas-equivalent production, or roughly 5 Mboe across the year.

Step 7 — Equivalent electricity

3.8 PJ × 0.60, the electrical efficiency of a state-of-the-art combined-cycle gas turbine, = 2.28 PJ of electricity, which is 633 GWh. This is the version that reaches the press release: "one shipload of gas, enough to power 250,000 European homes for a year".

Step 8 — Equivalent household heating

At about 1,200 m³ of gas per Dutch household per year (CBS 2024), the regasified 100 million m³ heats roughly 83,000 homes for a winter.

Eight units, one ship. The point is not to memorise the numbers — a professional looks those up — but to hold, with confidence, the fact that the same physical quantity stands behind every one of them. Read one unit and you read a corner of the industry. Read all eight and you read the industry.

Retrieval and generative practice

Answers to the recall questions are at the end. The generative prompt has no single right answer; the work is the reasoning.

Recall questions

1. A 250 MW onshore wind farm runs at a capacity factor of 32 per cent. Give its annual generation in GWh and in PJ.
2. A gas sale is priced at $14 per MMBtu on a higher heating-value basis. Express it in € per MWh on a lower heating-value basis, taking €0.92 per dollar and a 10 per cent gap between the two bases.
3. The IEA reports global oil supply of 4,700 Mtoe in 2024. Convert to exajoules and to millions of barrels of oil equivalent.

Generative-practice prompt

An LNG sponsor sanctions a new train of 7 million tonnes a year. A power investor asks how many gigawatts of dispatchable electricity it could underpin; a gas regulator asks how many billion cubic metres of regasified gas it adds to European supply; a climate analyst asks how many tonnes of CO₂ its burned output emits. Write a one-page memo answering all three with explicit conversion arithmetic, stating the heating-value basis in each answer, and flag the figure most sensitive to the lower-versus-higher choice.

Further reading

• International Energy Agency. Energy Statistics Manual. The canonical specification of the IEA's unit conventions, including the net basis for the tonne of oil equivalent and the factors linking Mtoe, exajoules and terawatt-hours.
• Smil, Vaclav. 2017. Energy and Civilization: A History. The energy-density tables in chapters 5 and 6 anchor the mass and volume conversions in physical reality.
• Energy Institute. 2025. Statistical Review of World Energy, 74th edition. Its conversion-factors appendix is the industry's working Rosetta stone between Mtoe, EJ, TWh and the major fuel volumes and masses.
• International Gas Union. 2025. World LNG Report. A reading exercise in MMBtu, MTPA, m³ of liquid and Nm³ of gas, all four units running through a hundred pages of narrative.
• S&P Global Commodity Insights. LNG Methodology and Specifications Guide. The pricing-agency document that specifies how the Japan-Korea Marker treats heating-value conversions, and the difference between a price quoted on the lower and the higher basis.

References

Citations follow the Chicago Author-Date convention. Where a figure was checked against a current web source, the access date is given.

• CBS (Centraal Bureau voor de Statistiek). 2024. Energieverbruik particuliere woningen; woningtype en regio's. Statline table 81528NED. The Hague: CBS. Accessed 22 May 2026.
• Energy Institute. 2025. Statistical Review of World Energy, 74th edition. London: Energy Institute.
• IEA. 2024a. Energy Statistics Manual. Paris: International Energy Agency.
• IGU (International Gas Union). 2025. World LNG Report 2025. Barcelona: International Gas Union.
• S&P Global. 2024. LNG Methodology and Specifications Guide. London: S&P Global Commodity Insights.
• Smil, Vaclav. 2017. Energy and Civilization: A History. Cambridge, MA: MIT Press.

Answers to recall questions

The generative-practice prompt has no single correct answer.

1. 250 MW × 8,760 h × 0.32 = 700,800 MWh = 701 GWh. In petajoules: 701 × 3.6 × 10⁻³ = 2.52 PJ.
2. $14/MMBtu × 0.92 = €12.88/MMBtu on the higher basis. One MMBtu is 0.2931 MWh, so that is €43.9/MWh higher basis. The lower basis carries 10 per cent less energy, so the price per unit of delivered energy rises: €43.9 ÷ 0.90 = €48.8/MWh on the lower basis.
3. 4,700 Mtoe × 41.868 GJ/toe × 10⁶ = 1.968 × 10¹¹ GJ = 197 EJ. In barrels: 4,700 × 7.33 = 34,450 Mboe.

Key insight. Energy is one scalar quantity wearing a dozen different uniforms. Fluency is not memorising every conversion; it is holding four numbers — 41.868, 6.12, 1.055, 3.6 — and always knowing which silent assumption, the lower heating value or the higher, is standing behind the figure in front of you.